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We study the prediction of the dark matter power spectrum at two-loop orderin the Effective Field Theory of Large Scale Structures (EFTofLSS) using highprecision numerical simulations. In our universe, short distance non-linearperturbations, not under perturbative control, affect long distancefluctuations through an effective stress tensor that needs to be parametrizedin terms of counterterms that are functions of the long distance fluctuatingfields. We find that at two-loop order it is necessary to include threecounterterms: a linear term in the over density, $\delta$, a quadratic term,$\delta^2$, and a higher derivative term, $\partial^2\delta$. After theinclusion of these three terms, the EFTofLSS at two-loop order matchessimulation data up to $k\simeq 0.34 \,h\, {\rm Mpc}^{-1}$ at redshift $z=0$, upto $k\simeq 0.55\,h\, {\rm Mpc}^{-1}$ at $z=1$, and up to $k\simeq 1.1\,h\,{\rm Mpc}^{-1}$ at $z=2$. At these wavenumbers, the cosmic variance of thesimulation is at least as small as $10^{-3}$, providing a high precisioncomparison between theory and data. The actual reach of the theory is affectedby theoretical uncertainties associated to not having included higher orderterms in perturbation theory, for which we provide an estimate, and bypotentially overfitting the data, which we also try to address. Since in theEFTofLSS the coupling constants associated with the counterterms are unknownfunctions of time, we show how a simple parametrization gives a sensibledescription of their time-dependence. Overall, the $k$-reach of the EFTofLSS ismuch larger than previous analytical techniques, showing that the amount ofcosmological information amenable to high-precision analytical control might bemuch larger than previously believed.

Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations